D22 2⁄3 in hieroglyphs Mathematical notation was decimal, and based on hieroglyphic signs for each power of ten up to one million. Each of these could be written as many times as necessary to add up to the desired number; so to write the number eighty or eight hundred, the symbol for ten or one hundred was written eight times respectively.[195] Because their methods of calculation could not handle most fractions with a numerator greater than one, they had to write fractions as the sum of several fractions. For example, they resolved the fraction two-fifths into the sum of one-third + one-fifteenth. Standard tables of values facilitated this.[196] Some common fractions, however, were written with a special glyph—the equivalent of the modern two-thirds is shown on the right.[197] Ancient Egyptian mathematicians had a grasp of the principles underlying the Pythagorean theorem, knowing, for example, that a triangle had a right angle opposite the hypotenuse when its sides were in a 3–4–5 ratio.[198] They were able to estimate the area of a circle by subtracting one-ninth from its diameter and squaring the result: Area ≈ [(8⁄9)D]2 = (256⁄81)r 2 ≈ 3.16r 2, a reasonable approximation of the formula π''r 2.[198][199] The golden ratio seems to be reflected in many Egyptian constructions, including the pyramids, but its use may have been an unintended consequence of the ancient Egyptian practice of combining the use of knotted ropes with an intuitive sense of proportion and harmony.[200] |
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